Modelling redshift-space distortion in the post-reionization $\mathrm{HI}$ 21-cm power spectrum

Abstract

The post-reionization $\mathrm{HI}$ 21-cm signal is an excellent candidate for precision cosmology, this however requires accurate modelling of the expected signal. Sarkar et al. (2016) have simulated the real space $\mathrm{HI}$ 21-cm signal, and have modelled the $\mathrm{HI}$ power spectrum as $P_{\mathrm{HI}}(k)=b^{2}P(k)$ where $P(k)$ is the dark matter power spectrum and $b(k)$ is a (possibly complex) scale dependent bias for which fitting formulas have been provided. This paper extends these simulations to incorporate redshift space distortion and predict the expected redshift space $\mathrm{HI}$ 21-cm power spectrum $P_{\mathrm{HI}}^s(k_{\perp },k_{\parallel })$ using two different prescriptions for the $\mathrm{HI}$ distributions and peculiar velocities. We model $P_{\mathrm{HI}}^s(k_{\perp },k_{\parallel })$ assuming that it is the product of $P_{\mathrm{HI}}(k)=b^{2}P(k)$ with a Kaiser enhancement term and a Finger of God (FoG) damping which has ${\sigma }_p$ the pair velocity dispersion as a free parameter. Considering several possibilities for the bias and the damping profile, we find that the models with a scale dependent bias and a Lorentzian damping profile best fit the simulated $P_{\mathrm{HI}}^s(k_{\perp },k_{\parallel })$ over the entire range $1\le z\le 6$. The best fit value of ${\sigma }_p$ falls approximately as $(1+z{)}^{-m}$ with $m=2$ and $1.2$ respectively for the two different prescriptions. The model predictions are consistent with the simulations for $k<0.3{\mathrm{Mpc}}^{-1}$ over the entire $z$ range for the monopole $P_0^s(k)$, and at $z\le 3$ for the quadrupole $P_2^s(k)$. At $z\ge 4$ the models underpredict $P_2^s(k)$ at large $k$, and the fit is restricted to $k<0.15{\mathrm{Mpc}}^{-1}$.

arXiv comment14 pages, 7 figures, 2 Tables, accepted for publication in MNRAS main journal

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